# Volume 1, Number 2, 2022 (Special Issue on "Investigations on Hermitian and Skew-Hermitian Systems")

### The c-equivalence principle and its implications for physics

**Abstract**

The c-equivalence principle, commonly accepted as true by most physicists, is the unstated assumption that equals the kinematic speed of light. Should someone prove the principle false, it would render the composition of two Lorentz transformations meaningless. The second hypothesis of the Special Theory of Relativity in its strong

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The c-equivalence principle, commonly accepted as true by most physicists, is the unstated assumption that equals the kinematic speed of light. Should someone prove the principle false, it would render the composition of two Lorentz transformations meaningless. The second hypothesis of the Special Theory of Relativity in its strong form would also be invalidated. This paper examined some of the consequences for physics, should this principle be proven false and outline some experiments to determine light speed, which could falsify the principle and provide evidence for the ether.Full article

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Review Article

### Quantum Properties of Coherently Driven Three-Level Atom Coupled to Vacuum Reservoir

**Abstract**

A three-level laser with an open cavity and a two-mode vacuum reservoir is explored for its quantum properties. Our investigation begins with a normalized order of the noise operators associated with the vacuum reservoir. The master equation and linear operators' equations of motion are used to determine the equations of

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A three-level laser with an open cavity and a two-mode vacuum reservoir is explored for its quantum properties. Our investigation begins with a normalized order of the noise operators associated with the vacuum reservoir. The master equation and linear operators' equations of motion are used to determine the equations of evolution of the atomic operators' expectation values. The equation of motion answers are then used to calculate the mean photon number, photon number variance, and quadrature variance for single–mode cavity light and two–mode cavity light. As a result, for γ=0, the quadrature variance of light mode

**a**is greater than the mean photon number for two-mode cavity light. As a result, for the two-mode cavity light, the maximum quadrature squeezing is 43.42 percent.Full article**Figures**

Article

### Relativistic Radial Density Theory (RRDT)

**Abstract**

Starting with Planck scale it is developed the Relativistic Radial Density Theory (

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*RRDT*). In this theory, the Planck and gravitational parameters can be described as the functions of the radial mass (energy) density value. This density is maximal at the minimal radius and minimal at the maximal radius. This conclusion
Starting with Planck scale it is developed the Relativistic Radial Density Theory (

*RRDT*). In this theory, the Planck and gravitational parameters can be described as the functions of the radial mass (energy) density value. This density is maximal at the minimal radius and minimal at the maximal radius. This conclusion is based on the fact that the ratio of Planck mass and Planck length (radius) is constant. These radiuses can be described as the function of the energy conservation constant*κ*. Using*RRD**T*, it is possible to develop the connections between Planck’s and gravitational parameters as function of the maximal and minimal radial mass (energy) density values. In that sense, the gravitational length, time, energy and temperature can be presented as the function of the Planck length, time, energy and temperature, respectively. This opens possibility to merge of Quantum Field Theory (*QFT*) and the General Theory of Relativity (*GTR*) at the quantum scale in gravitational field. The existence of the maximal radial mass (energy) density value at the minimal radius in gravitational field means that no singularity in that field. Further, the existence of the minimal radial mass (energy) density value at the maximal radius in gravitational field means that no infinity in that field. It follows the postulation: the most minimal radius in a gravitational field belongs to the minimal mass (energy). Since the Planck mass is not the minimal mass in space-time, the Planck length/radius is not the minimal length/radius in the space-time. If the calculated minimal (or maximal) radius is the bigger than the related official radius it means that there exists a dark matter in this object. In that sense, the black holes are presenting the state of the matter at the minimal radius where we have the maximal radial mass (energy) density value. Further, the maximal possible radius of the matter is presenting the state with the minimal radial mass (energy) density value. Thus, the maximal and minimal radial mass (energy) density values are constants and conserved items. Now the question is: do motion of the Universe follows the*RRD**T*?Full article
Article

### Role of Skew-Symmetric Differential Forms in Mathematical Physics and Field Theory

**Abstract**

Skew-symmetric differential forms possess properties that enable one to carry out a qualitative investigation of the equations of mathematical physics and the foundations of field theories. In the paper we call attention to a unique role in field theory of closed exterior skew-symmetric differential forms, which correspond to conservation laws

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Skew-symmetric differential forms possess properties that enable one to carry out a qualitative investigation of the equations of mathematical physics and the foundations of field theories. In the paper we call attention to a unique role in field theory of closed exterior skew-symmetric differential forms, which correspond to conservation laws for physical fields (to conservative quantities). At the same time, it was shown that such closed exterior forms can be derived from skew-symmetric differential forms, which follow from the mathematical physics equations describing material media such as thermodynamic, gas-dynamic, cosmic media. This points a connection the field theory equations with the mathematical physics equations. Such connection discloses the properties and specific features of field theory.Full article

Article

ISSN: 2834-5479

DOI prefix: 10.31586/ujpr

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